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(Revision of IEEE Std C57.96-1999)

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IEEE Std C57.96™-2013 (Revision of IEEE Std C57.96-1999)

IEEE Guide for Loading Dry-Type Distribution and Power Transformers Sponsor

Transformers Committee of the

IEEE Power and Energy Society Approved 11 December 2013 2013

IEEE-SA Standards Board


Abstract: General recommendations for the loading of dry-type distribution and power transformers installed in ventilated, non-ventilated, and sealed type enclosures are included in this standard. Keywords: ambient temperature, constant load, hottest-spot temperature, IEEE C57.96™, loading capability, loading transformer, rated output, resin-encapsulated, solid-cast transformer, time constant, transient loading

•

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Participants At the time this IEEE guide was completed, the Dry-Type Distribution and Power Transformer Loading Working Group had the following membership: Richard P. Marek , Chair James Antweiler Robert Ballard Carl Bush Terry Drees Derek Foster Juan Gutierrez Timothy Holdway Mike Iman John John

Charles Johnson Aleksandr Levin Donald MacMillan Rogelio Martinez Aniruddha Narawane Martin Navarro Dhiru Patel Paulette Powell

Lewis Powell Mangesh Rajadhyaksha Anil Sawant Sanjib Som David Stankes Kerwin Stretch Vijay Tendulkar Robert Thompson Albert Walls

The following members of the individual balloting committee voted on this guide. Balloters may have voted for approval, disapproval, or abstention. James Antweiler Robert Ballard Peter Balma Jeffrey Benach Wallace Binder Thomas Bishop Thomas Blackburn Carl Bush William Byrd Thomas Callsen Paul Cardinal John Crouse Glenn Davis Ray Davis Gary Donner Henry Earle Dan Evans Rabiz Foda Joseph Foldi Marcel Fortin Derek Foster Doaa Galal Jalal Gohari Randall Groves Bal Gupta Ajit Gwal Charles Haahr David Harris

Roger Hayes Gary Heuston Timothy Holdway Jill Holmes Philip Hopkinson John Houdek John John Charles Johnson Laszlo Kadar Sheldon Kennedy Yuri Khersonsky Jim Kulchisky Saumen Kundu John Lackey Chung-Yiu Lam Stephen Lambert Aleksandr Levin Thomas Lundquist Richard P. Marek Omar Mazzoni Daniel Mulkey Jerry Murphy K. R. M. Nair Martin Navarro Arthur Neubauer Michael Newman Raymond Nicholas Joe Nims

Lorraine Padden Bansi Patel Wesley Patterson Paulette Powell Brian Penny Alvaro Portillo Iulian Profir Michael Roberts Charles Rogers Oleg Roizman John Rossetti Thomas Rozek Bartien Sayogo James Smith Jerry Smith David Stankes Gary Stoedter Radoslaw Szewczyk David Tepen Robert Thompson John Vergis Jane Verner Tony Weekes Kenneth White Roger Wicks James Wilson Jian Yu Kipp Yule

vi

Copyright © 2014 IEEE. All rights reserved.


When the IEEE-SA Standards Board approved this guide on 11 December 2013, it had the following membership: John Kulick, Chair David J. Law, Vice Chair Richard H. Hulett, Past Chair Konstantinos Karachalios, Secretary Masayuki Ariyoshi Peter Balma Farooq Bari Ted Burse Stephen Dukes Jean-Philippe Faure Alexander Gelman

Mark Halpin Gary Hoffman Paul Houzé Jim Hughes Michael Janezic Joseph L. Koepfinger* Oleg Logvinov Ron Petersen

Gary Robinson Jon Walter Rosdahl Adrian Stephens Peter Sutherland Yatin Trivedi Phil Winston Yu Yuan

*Member Emeritus

Also included are the following nonvoting IEEE-SA Standards Board liaisons: Richard DeBlasio, DOE Representative Michael Janezic, NIST Representative Patrick Gibbons IEEE Standards Program Manager, Document Development Erin Spiewak IEEE Standards Program Manager, Technical Program Development

vii



Introduction This introduction is not part of IEEE Std C57.96-2013, IEEE Guide for Loading Dry-Type Distribution and Power Transformers.

This guide covers the loading of dry-type distribution and power transformers and has been developed to cover modern dry-type transformers through 10 000 kVA. The insulation systems referred to in this document meet the thermal evaluation criteria established by the now withdrawn IEEE Std C57.12.56™1986a or the replacement document, IEEE Std C57.12.60™. Work completed by the IEEE Insulation Life Subcommittee, comprising life test on transformer models, is the basis for the insulation life versus temperature relationship, designated as minimum life expectancy in IEEE Std C57.12.56-1986 and IEEE C57.12.60, which in turn are based on the Arrhenius reaction rate theory. To avoid ambiguity, this guide will use the term “life expectancy” to indicate the life to be expected at a given temperature. The “normal life expectancy” at rated hottest-spot temperature in a 30 °C ambient is expected to be 20 years. For calculation purposes, 180 000 h is used as the expected lifetime. This revision of the guide combined the content for all dry-type transformers, including those with solidcast and/or resin-encapsulated epoxy windings into the main body of the document. In addition, the computer programs in Annex B have been updated to include all transformer types, and detailed examples of loading and aging have been provided in Annex C. Moreover, the document has been updated to reflect the current IEEE Style Guide format.

a

Information on references can be found in Clause 2.

viii



Contents

1. Overview .................................................................................................................................................... 1 1.1 Scope ................................................................................................................................................... 1 1.2 Purpose ................................................................................................................................................ 1 2. Normative references.................................................................................................................................. 1 3. Definitions .................................................................................................................................................. 2 4. Overview .................................................................................................................................................... 2 4.1 General information............................................................................................................................. 2 4.2 Transformer life expectancy ................................................................................................................ 3 4.3 Transformer rated output ..................................................................................................................... 3 4.4 Aging of insulation .............................................................................................................................. 4 4.5 Ambient temperature ........................................................................................................................... 4 5. Loading equations ...................................................................................................................................... 5 5.1 Continuous loading.............................................................................................................................. 5 5.2 Transient loading ................................................................................................................................. 6 5.3 Time constants ..................................................................................................................................... 7 5.4 Calculation of loading capability ......................................................................................................... 8 6. Loading based on life expectancy ............................................................................................................ 12 6.1 Basic conditions................................................................................................................................. 12 6.2 Factors affecting transformer life ...................................................................................................... 12 6.3 Lifetime ............................................................................................................................................. 13 6.4 Example deriving lifetime calculation constants ............................................................................... 14 6.5 Method of converting actual load cycle to equivalent constant load ................................................. 15 6.6 Temperature limits for loading above rating ..................................................................................... 17 6.7 Daily load calculations ...................................................................................................................... 18 6.8 Other limitations................................................................................................................................ 19 Annex A (informative) Bibliography ........................................................................................................... 20 Annex B (informative) Computer programs................................................................................................. 21 B.1 Short time loading based on nameplate rating .................................................................................. 21 B.2 Loading above rating to give normal life expectancy during a one-day period ................................ 23 Annex C (informative) Example calculations .............................................................................................. 27 C.1 Overloads at constant temperature .................................................................................................... 27 C.2 Short time overload for a step change in load ................................................................................... 28 C.3 Life analysis with variable loads ....................................................................................................... 31

ix




IEEE Guide for Loading Dry-Type Distribution and Power Transformers IMPORTANT NOTICE: IEEE Standards documents are not intended to ensure safety, security, health, or environmental protection, or ensure against interference with or from other devices or networks. Implementers of IEEE Standards documents are responsible for determining and complying with all appropriate safety, security, environmental, health, and interference protection practices and all applicable laws and regulations. This IEEE document is made available for use subject to important notices and legal disclaimers. These notices and disclaimers appear in all publications containing this document and may be found under the heading “Important Notice” or “Important Notices and Disclaimers Concerning IEEE Documents.” They can also be obtained on request from IEEE or viewed at http://standards.ieee.org/IPR/disclaimers.html .

1. Overview

1.1 Scope This guide covers general recommendations for the loading of dry-type distribution and power transformers installed in ventilated, non-ventilated, and sealed type enclosures.

1.2 Purpose This document provides users with guidelines and limitations for loading dry-type transformers according to nameplate rating. Guidance is also provided for assessing the risks and consequences of loading above nameplate rating.

2. Normative references The following referenced documents are indispensable for the application of this document (i.e., they must be understood and used, so each referenced document is cited in text and its relationship to this document is explained). For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments or corrigenda) applies.

1



IEEE Std C57.96-2013 IEEE Guide for Loading Dry-Type Distribution and Power Transformers

IEEE Std C57.12.01™, IEEE Standard General Requirements for Dry-Type Di stribution and Power Transformers, Including Those with Solid-Cast and/or Resin Encapsulated Windings. 12 IEEE Std C57.12.56™-1986, IEEE Standard Test Procedure for Thermal Evaluation of Insulation Systems for Ventilated Dry-Type Power and Distribution Transformers. IEEE Std C57.12.60™, IEEE Standard Test Procedure for Thermal Evaluation of Insulation Systems for Dry-Type Power and Distribution Transformers, Including Open-Wound, Solid-Cast, and ResinEncapsulated Transformers. IEEE Std C57.94™, IEEE Recommended Practice for Installation, Application, Operation, and Maintenance of Dry-Type General Purpose Distribution and Power Transformers. IEEE Std C57.110™, IEEE Recommended Practice for Establishing Liquid-Filled and Dry-Type Power and Distribution Transformer Capability When Supplying Nonsinusoidal Load Currents. IEEE Std C57.134™, IEEE Guide for Determination of Hottest-Spot Temperature in Dry-Type Transformers.

3. Definitions

For the purposes of this document, the following terms and definitions apply. The IEEE Standards Dictionary Online should be consulted for terms not defined in this clause. 3 dry-type transformer: A transformer in which the core and coils are in a gaseous or dry compound insulating medium. non-ventilated dry-type transformer: A dry-type transformer that is so constructed as to provide no intentional circulation of external air through the transformer and operating at zero gauge pressure. sealed transformer: A dry-type transformer with a hermetically sealed tank. ventilated dry-type transformer: A dry-type transformer that is so constructed that the ambient air may circulate through its enclosure to cool the transformer core and windings.

4. Overview

4.1 General information

The recommendations given in this guide are based solely on the thermal characteristics of dry-type transformers. The insulation systems referred to in this document meet the thermal evaluation criteria established by the now withdrawn IEEE Std C57.12.56-1986 4 or the replacement document, IEEE Std C57.12.60.

1

The IEEE standards or products referred to in this clause are trademarks of The Institute of Electrical and Electronics Engineers, Inc. IEEE publications are available from The Institute of Electrical and Electronics Engineers, 445 Hoes Lane, Piscataway, NJ 08854, USA (http://standards.ieee.org/). 3 IEEE Standards Dictionary Online subscription is available at: http://www.ieee.org/portal/innovate/products/standard/standards_dictionary.html. 4 Information on references can be found in Clause 2. 2

2




Loads above rating, based on this guide, may be applied only after a thorough study has been made of all the other various limitations that may be involved. Among these limitations are gas expansion and pressure in sealed dry-type units; the thermal capability of associated equipment, such as bushings, leads, connections, tap changers in all dry-type transformers; and ancillary equipment, such as cables, reactors, circuit breakers, disconnecting switches, and current transformers. Also, limitations may be imposed by voltage regulation necessary for satisfactory operation of connected apparatus and by the increased operating costs due to the higher losses accompanying loads above nameplate rating. These may constitute the practical limit on load-carrying ability and should be considered before applying loads in excess of nameplate rating. It is intended that dry-type transformers be installed based on the recommendations given in IEEE Std C57.94. If dry-type transformers are installed in subsurface vaults or areas of minimum size where the natural ventilation will significantly raise ambient temperature with changes in transformer losses, the increase in effective ambient temperature for expected increased transformer losses must be determined before loading limitations can be estimated. Dry-type transformers are generally designed to permit loading in line with these guides, but if there are any questions as to the capability of a particular transformer to carry the desired load, the manufacturer should be consulted for specific recommendations.

4.2 Transformer life expectancy Recommendations in this guide are based on the life expectancy of transformer insulation as affected by operating temperature and time and do not consider other factors that may affect transformer life, such as voltage stress or mechanical stress especially due to system voltage fluctuations or system faults. The loading capability of transformers is related to properties of the insulating materials and insulation systems. Transformer life expectancy is not accurately known for many reasons, but primarily due to varying loads and operating temperatures over the life of a typical unit. However, the information given regarding loss of life of the insulation is better understood, is considered to be conservative, and is the best that can be produced from present knowledge of the subject. (The word “conservative” is used in the sense that the expected loss of insulation life for recommended load will not be greater than the amount stated.)

4.3 Transformer rated output The rated kilovolt-ampere output of a transformer is the load that it can deliver continuously at rated secondary voltage and rated frequency without exceeding the specified temperature rise under usual service conditions, as described in IEEE Std C57.12.01. The term “rated output” or “rated load” used in this guide refers to nameplate rating of continuously rated transformers. For transformers that do not have a continuous rating or when such information is not indicated on the nameplate or the transformer operating manual, the manufacturer should be consulted for additional information. The temperature rise on which the rating is based takes into consideration industry experience regarding the insulation life as affected by operating temperature and the ambient temperature assumed to exist throughout the life of the transformer. The actual output that a transformer can deliver at any time in service without undue deterioration of the insulation may be more or less than the rated output, depending upon insulation temperature rating, the ambient temperature, altitude, and other attendant operating conditions.

3




4.4 Aging of insulation Aging or deterioration of insulation is a function of time and temperature. Since in most apparatus the temperature is not uniform, the part that is operating at the highest temperature will ordinarily undergo the greatest deterioration. Therefore, aging studies consider the aging effects produced by the highest temperature. In the transformer winding, this is known as the hottest-spot temperature. Additional information on how to determine the hottest-spot temperature for dry-type transformers may be found in IEEE Std C57.134. Practically all of the data in reference to the aging of insulation at different temperatures has been obtained in laboratory tests in which the changes in mechanical or electrical properties, or both, have been measured. The relation between the life expectancy of insulation as indicated by laboratory tests and the actual life of a transformer is largely theoretical. Thus, loading based on such information should be tempered by sound judgment based on experience. Because the cumulative effects of temperature and time in causing deterioration of transformer insulation are not thoroughly established, it is not possible to predict with a great degree of accuracy the length of life of a transformer, even under constant or closely controlled conditions, much less under widely varying service conditions. However, the cumulative effects of repeated or long-time higher-than-normal operating temperatures can lead to deterioration of the mechanical and dielectric properties of the insulation. If this deterioration proceeds far enough, it may significantly reduce the life of the transformer, particularly if the apparatus is subjected to system short-circuits or over-voltage stresses. The change in rate of deterioration with change in temperature has been widely studied, but the amount of change in actual transformer life with a change in operating temperature remains debatable. However, there is agreement that, in all of the methods of calculating the effect of operating temperature on insulation life, higher than normal operating temperatures, whether they are due to loads above rating or to high ambient temperatures, result in some reduction in transformer life. The many variables mentioned, and particularly the many varying conditions of load and ambient to which a transformer can be subjected in service, make it impossible to give precise rules for the loading of transformers. However, it is possible to give suggested loading under specified conditions to assist the user in making informed loading decisions.

4.5 Ambient temperature Ambient temperature is an important factor in determining the load capability of a transformer, since the temperature rise for any load must be added to the ambient to determine the operating temperature. Whenever the actual ambient temperature can be determined from readings taken at the time of the load pattern being considered, such temperatures should be used to determine the winding hottest-spot temperature and the load capability of the transformer. It is often necessary to predict the load that a transformer can carry with no sacrifice of life expectancy at some future time when the actual ambient temperature is unknown. For dry-type transformers used in indoor installations, the ambient temperature can be approximated from heating or air conditioning records of the installation. For transformers used outdoors, the ambient temperature for the month in which the expected load is anticipated can be obtained from reports gathered by the Climatic Services Branch of the National Climatic Data Center, which is a part of the National Oceanic and Atmospheric Administration [B6]. These reports are available for areas throughout the world. These ambient temperatures should be used as follows: 

For loads with normal life expectancy, use the average temperature over a period of years for the month involved. 4






For short-time loads above rating with moderate sacrifice of life expectancy, use the average of the daily maximum temperatures for the month involved averaged with similar values for the same month over a period of years.

5. Loading equations

5.1 Continuous loading The hottest-spot winding temperature may be calculated by Equation (1):

Θ HS

= Θa + Δ Θ HS

(1)

where, Θ HS Θ a ∆Θ HS

is the hottest-spot winding temperature, in °C is the ambient temperature, in °C is the hottest-spot temperature rise over ambient, in °C

The hottest-spot temperature rise as a function of load for steady-state conditions and self-cooled operation may be calculated by Equation (2) through Equation (4):

ΔΘ HS = ΔΘ HS ,r ×

[L]2m

(2)

where, ∆Θ HS ∆Θ HS,r

L m

is the hottest-spot temperature rise over ambient, in °C is the rated hottest-spot temperature rise over ambient at 1.0 per unit load, in °C is the per unit load is an empirical constant (0.8 is suggested unless another value can be justified by test data)

Fan-cooled operation is calculated as follows:

[

Δ Θ HS = Δ Θ HS ,r × L

2

K T

]

X

(3)

where, ∆Θ HS ∆Θ HS,r

L K T X

is the hottest-spot temperature rise over ambient, in °C is the rated hottest-spot temperature rise over ambient at 1.0 per unit load, in °C is the per unit load is the temperature correction for resistance change with temperature is an empirical constant used in forced-air calculation (1.0 is suggested unless another value can be justified by test data)

5




K T =

T k + Δ Θ HS T k + Δ Θ HS , r

(4)

where, K T ∆Θ HS ∆Θ HS,r

T k

is the temperature correction for resistance change with temperature is the hottest-spot temperature rise over ambient, in °C is the rated hottest-spot temperature rise over ambient at 1.0 per unit load, in °C is the temperature constant for conductor (225 for aluminum and 234.5 for copper)

Test data indicates that Equation (2) through Equation (4), although only approximate, should result in conservative predictions of the hottest-spot temperature. The m exponent of 0.8 for self-cooled operation and the X exponent of 1.0 for forced-air operation are derived from heat transfer correlations for natural and forced convection. Test data indicates that a temperature correction for resistance given by Equation (4) is required to predict hottest-spot temperatures during forced-air loading due to the higher losses present at forced-cooled operation. Equation (2) and Equation (3) ignore eddy losses in the winding, which vary inversely with temperature. Eddy losses are usually less than 10% of the load losses unless harmonic currents are present. Equation (3) requires an iterative calculation procedure. Using the suggested exponents and considering the resistance change with temperature for fan-cooled operation should result in conservative calculations of the hottestspot temperature rise even when eddy losses are ignored. If harmonic currents are present, the increased eddy losses during overloading may need consideration in accordance with IEEE Std C57.110.

5.2 Transient loading The hottest-spot temperature due to transient overloading may be determined by Equation (5) and Equation (6):

∆Θt = (∆ΘU − ∆Θi )× 1 − exp − τ t + ∆Θi r

(5)

where, ∆Θ t ∆Θ i ∆Θ U

t τ r

is the hottest-spot temperature rise at some time t after the overload, in °C is the initial hottest-spot rise at some prior load Li, in °C is the ultimate hottest-spot rise if the per u nit overload LU , continued until the hottest-spot temperature stabilized, in °C is the time, in minutes is the time constant in minutes for the transformer at rated load

Θ HS = Δ Θt + Θa

(6)

where, Θ HS ∆Θ t

Θ a

is the hottest-spot temperature, in °C is the hottest-spot temperature rise at some time t after the overload, in °C is the ambient temperature, in °C

6




5.3 Time constants The concept of a transformer time constant is based on the assumption that a single heat source supplies heat to a single heat sink and that the temperature rise of the sink is an exponential function of the heat input. The time constant is the time required for the temperature of the winding to reach 63.2% of a stabilized temperature at any load. In this context, the time constant is the time required for the temperature rise over ambient to change 63.2% after a step change in load. For loading purposes, it is desirable to have as large a time constant as possible. Hottest-spot temperature calculations for loading should be made on both the low-voltage and high-voltage windings, since published test data indicates that the time constants may be different. Insulation system temperature classes for the two windings may also be different. The time constant of a winding at rated load may be estimated by the Equation (7):

τ r =

C ∆Θ HS , r − Θe

P r

(7)

where is the time constant in minutes for the transformer at rated load is the effective thermal capacity of winding, in watt-minutes per K (Wmin/K), [15.0 × mass of aluminum conductor in kilograms (kg)] + [24.5 × mass of epoxy and/or other winding insulation in kilograms (kg)], or [6.42 × mass of copper conductor in kilograms (kg)] + [24.5 × mass of epoxy and/or other winding insulation in kilograms (kg)] is the I 2 R loss of a winding at rated load and rated temperature rise, in watts is the rated hottest-spot temperature rise over ambient at 1.0 per unit load, in °C is the core contribution to winding hottest-spot temperature rise at rated load, in °C (5 °C for outer winding, other values may be used if test data is available) (25 °C for inner winding, other values may be used if test data is available)

τ r

C

P r ∆Θ HS,r

Θ e

The time constant for any load and for any starting temperature for either a heating cycle or a cooling cycle may be estimated by Equation (8).

τ = τ r ×

∆Θ U ∆Θ HS ,r

(

∆Θ U

∆Θ HS ,r

−

) −( 1 m

∆Θ i ∆Θ HS ,r ∆Θ i

∆Θ HS ,r

)

1 m

(8)

where, τ τ r ∆Θ U ∆Θ i ∆Θ HS,r

m

is the time constant in minutes for the transformer at any load is the time constant in minutes for the transformer at rated load is the ultimate hottest-spot rise if the per u nit overload LU , continued until the hottest-spot temperature stabilized, in °C is the initial hottest-spot rise at some prior load Li, in °C is the rated or tested hottest-spot temperature rise over ambient at 1.0 per unit load, in °C is an empirical constant, which is equal to 0.8 (suggested unless test data is available)

Time constants may also be estimated from the hot resistance cooling curve obtained during thermal tests. The manufacturer may also be consulted for more accurate estimations of the winding time constants than

7




estimated by Equation (7) and Equation (8). Consideration may be given to specifying that time constants be shown on test reports when supplied.

5.4 Calculation of loading capability

5.4.1 Loading in standard conditions Equation (1) through Equation (8) may be used to determine hottest-spot temperatures during overloads. They may also be used to determine the short-time or continuous loading. The initial hottest-spot rise for prior load Li may be obtained from Equation (2). It is determined in Equation (9):

∆Θi = ∆Θ HS , r × [Li ]2 m

(9)

where, is the hottest-spot temperature rise at the prior per unit load, in °C is the rated hottest-spot temperature rise over ambient at 1.0 per unit load, in °C is the prior per unit load is an empirical constant, which is equal to 0.8 (suggested unless test data is available)

∆Θ i ∆Θ HS,r

Li m

From Table 1, select the rated hottest-spot winding temperature.

Table 1 — Constants for lifetime equation Insulation system temperature °C 130 150 180 200 220

Rated hottestspot winding temperature °C 120 140 170 190 210

Arrhenius’ equation constants 6 °C ln(a) –34.011 –36.321 –39.787 –42.098 –44.408

8 °C

b 18 129 20 006 22 994 25 102 27 302

ln(a) –22.656 –24.389 –26.988 –28.721 –30.454

10 °C b 13 665 15 076 17 322 18 907 20 560

ln(a) –15.844 –17.230 –19.309 –20.696 –22.082

b 10 986 12 118 13 919 15 190 16 515

For the ambient temperature, determine the permissible hottest-spot temperature rise at time t from Equation (1), as shown in Equation (10). ∆Θt = Θ HS − Θa

(10)

where, ∆Θ t

Θ HS Θ a

is the hottest-spot temperature rise at time t , in °C is the hottest-spot winding temperature, in °C is the ambient temperature, in °C

Determine the ultimate hottest-spot temperature rise from Equation (5), as shown in Equation (11).

8




 ∆Θ − ∆Θ  ∆ΘU =  t t i  + ∆Θi  1− exp ( − τ ) 

(11)

where, is the ultimate hottest-spot rise if the per u nit overload LU , continued until the hottest-spot temperature stabilized, in °C is the hottest-spot temperature rise at some time t after the overload, in °C is the initial hottest-spot rise at some prior load Li, in °C is the duration of the overload, in minutes is the time constant in minutes for the transformer

∆Θ U ∆Θ t ∆Θ i

t τ

From Equation (2), the overload corresponding to these conditions may be obtained as in Equation (12):

LU =

[

]

1 2m

∆Θ U ∆Θ HS ,r

(12)

where, LU

is the overload in per unit load is the ultimate hottest-spot rise if the per u nit overload LU , continued until the hottest-spot temperature stabilized, in °C is the rated hottest-spot temperature rise over ambient at 1.0 per unit load, in °C is an empirical constant, which is equal to 0.8 (suggested unless test data is available)

∆Θ U ∆Θ HS,r

m

A similar derivation based on Equation (3) results in the Equation (13) for forced air operation:

1

LU =

 ∆ΘU  X  ∆Θ HS , r  K T

(13)

where, LU ∆Θ U ∆Θ HS,r

X K T

is the overload in per unit load is the ultimate hottest-spot rise if the per u nit overload LU , continued until the hottest-spot temperature stabilized, in °C is the rated hottest-spot temperature rise over ambient at 1.0 per unit load, in °C is an empirical constant used in forced-air calculation, which is 1.0 (suggested unless test data available) is the temperature correction for resistance change with temperature

9




5.4.2 Influence of ambient temperature The average ambient temperature should cover periods not exceeding 24 h, with the maximum temperature not more than 10 °C greater than the average temperature. For each degree Celsius that the average temperature of the cooling air is above or below 30 °C, a transformer may be loaded below or above its nameplate kilovolt-ampere rating for any period, as specified in Table 2. Loading based on ambient temperature with the loads permitted by Table 2 can give approximately the same life expectancy as if the transformers had been operated at nameplate rating and standard ambient temperatures over the same period. The operation of transformers in cooling air above 50 °C or below 0 °C is not covered by Table 2, and the manufacturer should be consulted for these operating conditions. Since the ambient temperature is an important factor in determining the load capability of a transformer, it should be controlled for indoor installations by adequate ventilation, and it should always be considered in outdoor installations.

Table 2 —Continuous per unit loading capability as a function of ambient temperature Cooling mode

24 h average ambient temperature °C

130

150

180

200

220

0

1.20

1.16

1.13

1.11

1.10

10

1.13

1.11

1.09

1.08

1.07

20

1.07

1.06

1.04

1.04

1.03

30

1.00

1.00

1.00

1.00

1.00

40

0.93

0.94

0.95

0.96

0.96

50

0.85

0.88

0.91

0.92

0.93

0

1.15

1.13

1.10

1.09

1.08

10

1.11

1.09

1.07

1.06

1.05

20

1.05

1.04

1.04

1.03

1.03

30

1.00

1.00

1.00

1.00

1.00

40

0.94

0.95

0.96

0.97

0.97

50

0.88

0.90

0.93

0.94

0.94

AA, ANV

AA/FA, AFA

Insulation temperature class

NOTE—Cooling mode designations may be found in IEEE Std C57.12.01.

Table 2 per unit AA and ANV loading capability values are calculated from Equation (15) which is derived from Equation (1) and Equation (2) as in Equation (14):

Θ HS =Θ a

+ Δ Θ HS ,r × [L]

2m

(14)

Solving for the per unit load L, the equation then becomes:

L =

[

Θ HS

]

−Θ a 0.625

Δ Θ HS ,r

(15)

where, Θ HS Θ a

is the hottest-spot winding temperature, in °C, as defined in Table 1 is the ambient temperature, in °C, equal to the 24-h average ambient temperature in this case

10




is the rated or tested hottest-spot temperature rise over ambient at 1.0 per unit load, in °C is the per unit load is an empirical constant, which is equal to 0.8 (suggested unless test data is available)

∆Θ HS,r

L m

Table 2 per unit AA/FA and AFA loading capability values are calculated in a similar fashion from Equation (1) and Equation (3). Note, however, that the resistance temperature correction factor K T was not used to develop the table values, since these factors are intended to be estimates, and it would not be possible to properly vary the correction factor for the different temperature classes in a single table. More accurate load factors may be calculated for specific application conditions by using the reference equations with the proper resistance temperature correction factor.

5.4.3 Influence of altitude on loading Because dry-type transformers are dependent on air for dissipation of heat loss, the effect of decreased air density due to high altitude is to increase the temperature rise of the transformers. Transformers may be operated at rated kilovolt-amperes at altitudes greater than 1000 m without exceeding temperature limits, provided the average temperature of the cooling air does not exceed the values of Table 3 for the respective altitudes. The cooling air temperatures are based on an increase in average winding temperature rise of 0.5% for every 100 m above 1000 m altitude for natural cooling and 1.0% for forced-air cooling. The data included in Table 3 apply to ventilated dry-type and non-ventilated dry-type transformers only and are not applicable to sealed or gas-filled transformers. An altitude of 4500 m is considered a maximum for dry-type transformers conforming to IEEE Std C57.12.01.

Table 3 — Maximum allowable 24-h average temperature of cooling air in °C for operation at rated kilovolt-amperes with normal loss of life under unusual altitude conditions Insulation temperature class AA, ANV cooling

Rated average winding temperature rise °C

130

Altitude

1000 m

2000 m

3000 m

4000 m

75

30

26

23

19

150

90

30

26

21

17

180

115

30

24

19

13

200

130

30

24

17

11

220

150

30

23

15

8

Insulation temperature class AA/FA, AFA cooling

Rated average winding temperature rise °C

130

Altitude 1000 m

2000 m

3000 m

4000 m

75

30

23

15

8

150

90

30

21

12

3

180

115

30

19

7

-5

200

130

30

17

4

-9

220

150

30

15

0

-15

NOTE—Cooling mode designations may be found in IEEE Std C57.12.01

Transformers may be operated in a 30 °C ambient at altitudes greater than 1000 m without exceeding temperature limits, provided the load to be carried is reduced below rating by the percentages given in Table 4 for each 100 m that the altitude exceeds 1000 m. IEEE C57.12.01 only recognizes dry-type

11




transformer applications up to 4500 m. The transformer manufacturer should be consulted for applications above this altitude.

Table 4 — Rated kilovolt-ampere derating factors for altitudes greater than 1000 m at 30 °C average ambient temperature Type of cooling

Derating factor for each 100 m %

Self-cooled (AA, ANV)

0.3

Forced-air-cooled (AA/FA, AFA)

0.5

6. Loading based on life expectancy

6.1 Basic conditions The basic loading conditions of a transformer for normal life expectancy are as follows: 

The transformer is continuously loaded at rated kilovolt-amperes and rated delivered voltage.



The average temperature of the cooling air during any 24-h period is equal to 30 °C, and the temperature of the cooling air at no time exceeds 40 °C.



The altitude does not exceed 1000 m.

The hottest-spot temperature of the winding is the sum of the ambient temperature, the average temperature rise, and the hottest-spot allowance. For dry-type transformers operating continuously under the foregoing conditions, the rated hottest-spot temperature is 10 °C less than the temperature class, based on a 30 °C ambient temperature. IEEE Std C57.12.60 is the document that defines the test procedure for thermal evaluation of dry-type transformer insulation systems. Although the end point was arbitrarily set to 40 000 h, it should not be interpreted that this is also the life of the corresponding transformer. The resulting thermal index allows the comparison of different insulation systems in response to a very severe accelerated life test, intentionally designed to precipitate a failure within a reasonable length of time. Years of experience have indicated that a transformer rated in accordance with IEEE Std C57.12.01 and operated under the foregoing conditions are estimated to yield a normal life expectancy of 20 years o r more.

6.2 Factors affecting transformer life Dry-type transformers may be loaded above rated kilovolt-amperes under conditions other than those specified in the preceding clauses, with a sacrifice of life expectancy dependent on the load capability of the transformer and on the actual operating conditions. The overload capability of dry-type transformers varies widely and is affected by the following characteristics: 

Hottest-spot winding conductor rise over ambient



Ratio of load losses to no-load losses



Time constant



Ambient temperature

12




Operating conditions for dry-type transformers are so variable that no single set of practical loading data can be presented for all possible combinations of conditions and loading. However, methods are outlined in this clause whereby the user can estimate allowable loads for the user’s own conditions by taking into account the probable number and nature of such loads during the life of the transformer and the approximate percentage of life expectancy that the user is willing to sacrifice. Dry-type transformers may be loaded above their rated kilovolt-amperes, with a sacrifice of life expectancy, dependent upon the load capability of the transformer and on the actual operating conditions. When heat, which is mainly due to the transformer losses, is transferred to the insulation system, a chemical process begins. This process changes the molecular structure of the materials that form the insulation system. The aging rate increases with the amount of heat transferred to the system. This process is cumulative and irreversible, which means that the materials do not regain their original molecular structure when the heat supply stops and the temperature decreases. It is assumed that failing insulation due to aging is one of the causes of end of life of the transformer. It is also assumed that the aging rate varies with temperature according to the Arrhenius equation. The two constants in Arrhenius’ equation should ideally be determined by means of thermal endurance testing according to IEEE Std C57.12.60. Where such test data is not available, this guide provides estimated constants, which are calculated on the basis of the following assumptions: a)

General consensus is that a temperature increase of 6 °C for solid-cast and 10 °C for resinencapsulated transformers doubles the aging rate and are good estimated values for the whole winding linked with the value of specific materials used in the winding

b)

A tested value for this doubling rate should be used when determined by thermal endurance tests on the complete electrical insulation system

c)

180 000 h is taken as the normal life expectancy of approximating 20 years life operating at the rated hottest-spot temperature.

6.3 Lifetime The expected lifetime t Life of a transformer at a constant hottest-spot temperature T in Kelvin (K) can be calculated by means of the following Arrhenius equation [Equation (16)]: b

t Life =

a × e T

(16)

This equation can be more conveniently written as Equation (17):

 b   T  

t Life = a × exp

(17)

where t Life a b T e

is the expected lifetime in hours is a constant for different insulation system temperatures (ln(a) is given in Table 1 for ease of calculation) is a constant, given in Table 1, for different insulation system temperatures is the hottest-spot temperature in Kelvin (K) is the base of natural logarithms with the approximate value of 2.718 282

NOTE— Degrees Celsius may be converted to degrees Kelvin by adding 273.15.

13




Rearranged, this equation becomes Equation (18):

 b    T 

ln(t Life ) = ln(a) + 

(18)

6.4 Example deriving lifetime calculation constants The following illustrates the procedure for calculating the constants ln(a) and b for the rated hottest-spot temperature T, for the different insulation system temperatures in Table 1. Equation (20) and Equation (21) are taken from the base Equation (19), beginning with the assumed lifetime of 180 000 h and the half-life of 90 000 h. For a 220 insulation system with a halving constant of 10 °C, the hottest-spot temperature at 180 000 h is 210 °C and the hottest-spot temperature at 90 000 h is 220 °C. The constants for a range of insulation systems are shown in Table 1 with a 6 °C halving constant, corresponding to a typical solid-cast insulation system and a 10 °C halving constant, corresponding to a typical resin-encapsulated insulation system. The constants for a halving constant of 8 °C are also shown as an example of an insulation system with a non-typical halving constant.

ln(180 000) =

b

210 + 273.15

ln(90 000) =

+ ln(a) = 12.100712

(19)

b + ln(a) = 11.40756 210 + 10 + 273.15

(20)

Equation (19) and Equation (20) then become Equation (21) and Equation (22):

ln(a) = 12.100712 − ln(a) = 11.40756 −

b 483.15

b 493.15

(21)

(22)

Subtracting Equation (22) from Equation (21) results in:

0 = 12.100712 − 11.40756 −

b 483.15

+ 493b.15

(23)

b = 16 515.4

(24)

Substituting b into Equation (21) results in:

ln(a ) = 12.100712 − 34.1827 = − 22.082

(25)

14




6.5 Method of converting actual load cycle to equivalent constant load Permissible loading is a function of the initial load, the peak load and their durations. Each loading combination may be considered as a simple rectangular load cycle consisting of an essentially constant initial load followed by a rectangular peak of the magnitude and time given in the tables, with the load returning to the initial load at the end of the rectangular peak. The assumed loading for the calculations in the tables is illustrated in Figure 1.

Figure 1 — Assumed load cycle

The daily load cycle is more often similar to the cycle represented by the solid line in Figure 2 throughout the day and usually with one period in the daily load cycle when the load builds up to a considerably greater value than any reached at other times. Generally, the maximum value or peak load is not reached and passed suddenly but builds up and falls off gradually. To use the loading recommendations, the actual fluctuating load cycle must be converted to a thermally equivalent, simple rectangular load cycle, such as that represented by the dashed line in Figure 2. A transformer supplying a fluctuating load generates a fluctuating loss, the effect of which is about the same as that of an intermediate load held constant for the same period of time. This is due to the heat storage characteristics of the materials in the transformer. A load, generating losses at the same rate as the average rate caused by the fluctuating load, is an equivalent load from a temperature standpoint. Equivalent load for any portion of a daily load cycle may be expressed by Equation (26).

L EQ

( L12 t 1 + L22 t 2 + ... + L2n t n )  =  (t 1 + t 2 + ... t n ) 

0.5

(26)

where L1, L2, …, Ln t 1, t 2, …, t n

are the various load steps in percent, per unit, or in actual kilovolt-amperes are the duration of the loads, respectively.

Equivalent initial load is the root-mean-square (rms) load obtained by Equation (27) over a chosen period preceding the peak load. Experience with this method of load studies indicates that quite satisfactory results are obtained by considering the 12-h period preceding the peak in the determination of the equivalent initial load. With a time interval of 1 h suggested as a further simplification, the equation for a 12-h period becomes the following: 15




equivalent initital load

=

(

0.29 × L12 + L22

2

+ ... + L12

)

0 .5

(27)

where L1, L2, …, L12 are the average load by inspection for each 1-h interval of the 12-h period preceding peak load.

Figure 2 — Actual load cycle

Equivalent peak load for the usual load cycle is the rms load obtained by Equation (27) for the limited period over which the major part of the actual irregular peak seems to exist. The estimated duration of the peak has considerable influence over the rms peak value. If the duration is overestimated, the rms peak value may be considerably below the maximum peak demand. To guard against overheating due to high, brief overloads during the peak period, the rms value for the peak load should not be less than 90% of the integrated 0.5-h maximum demand. Loading factors greater than 2.0 per unit of the rated load are very severe and can cause many issues aside from reducing transformer life. Such loading should only be used as a last resort and with great care. If this situation arises, the user is advised to contact the manufacturer for analysis of the specific transformer and to seek expert advice. For this reason, a 2.0 per unit load is used as a limiting factor in this guide. Table 5 shows per unit load calculation results for a range of situations for various insulation temperature classes. The calculations are the result of the basic computer program detailed in B.1. The limiting factors are the 2.0 per unit load and a maximum hottest-spot temperature equal to the insulation system temperature class.

16




Table 5 — Examples of short-time overload based on rating not exceeding maximum hottest-spot temperature

Insulation system type

Insulation system temperature class

150 Resinencapsulated

180

220

130

Solid-cast

150

180

Peak load per unit

Prior stabilized load per unit

Peak load duration min

Time constant min

Ambient temperature °C

1.00 1.10 1.39 1.00 1.09 1.34 1.00 1.08 1.30 1.03 1.39 2.00 1.03 1.37 2.00 1.03 1.34 1.90

0.5 0.7 0.9 0.5 0.7 0.9 0.5 0.7 0.9 0.5 0.7 0.9 0.5 0.7 0.9 0.5 0.7 0.9

120 60 30 120 60 30 120 60 30 120 60 30 120 60 30 120 60 30

15 30 60 15 30 60 15 30 60 45 90 180 45 90 180 45 90 180

40 30 20 40 30 20 40 30 20 40 30 20 40 30 20 40 30 20

Max hottestspot temperature reached during load cycle °C

150

180

220

130

150

180

6.6 Temperature limits for loading above rating The actual output that a dry-type transformer can deliver at any time in service may be more or less than the rated kilovolt-ampere output depending upon the ambient temperature, altitude, and other attendant operating conditions. If the load and ambient temperatures are below rated, then an overload may be sustained at the hottest-spot temperature rating of the insulation class of the windings. This is described as rated temperature loading and should provide normal life expectancy. Loading that results in hottest-spot temperatures above the insulation temperature class is defined as loading above rating and can result in reduced life expectancy. The life expectancy decreases due to the total cumulative effect of operation at a hottest-spot temperature above rating and the time at elevated hottest-spot temperature. The manufacturer should be consulted for recommendations for maximum permissible hottest-spot temperatures for loading above rating for a specific transformer. However, Table 6 provides guidelines in the absence of specific information. Note that while solid-cast transformers perform very well in short time overload events due to the typically very long time constants, these transformers are susceptible to epoxy cracking during sustained excessive overloads, which could lead to catastrophic failure. Resin-encapsulated transformers typically overheat much more quickly and will survive very long periods of excessive overload but with the consequence of drastically reduced insulation life. Table 6 reflects these typical characteristics with different recommended maximum limiting hottest-spot temperatures for these two types of transformers.

17




Table 6 — Recommended temperature limits when loading beyond nameplate rating Insulation temperature class

130 150 180 200 220

Maximum hottest-spot rated temperature °C 120 140 170 190 210

Maximum hottest-spot temperature, loading above rating, °C Solid-cast Resin-encapsulated 155 200 175 220 205 250 225 270 N/A 290

6.7 Daily load calculations

6.7.1 Loading on the basis of short-time loads The permissible load on dry-type transformers may be increased above rated load for short times by the multipliers derived from the equations of Clause 5 and the computer program in Annex B.1, provided that: 

The short-time peak load occurs not more than once in any 24-h period.



The short-time peak load follows and is followed by either a constant load or an equivalent constant load.



The limitations of 6.6 and the basic conditions of 6.1 are met.

6.7.2 Effects of various factors existing at one time When two or more of the following factors affecting loading for normal life expectancy exist at one time, the effects are cumulative, and the increase in loads due to each may be added to secure the maximum suggested load. (Each increase must be based on rated kilovolt-amperes.) 

Loading on basis of ambient temperature



Loading on basis of measured temperature rise



Loading on basis of short-time loads above rating

6.7.3 Loading above rating to give normal life expectancy The data for Table 7 was determined by the computer program listed in Annex B.2 and was based on the following limitations: 

Maximum 1.0 per unit daily life



Maximum 2.0 per unit load



Maximum hottest-spot temperature per Table 6

18




Table 7 — Examples of daily loads above rating to give normal life expectancy Insulation system type

Insulation system temperature class

150 Resinencapsulated

180

220

130

Solid-cast

150

180

Load in excess of rating PU

Prior stabilized load %

Peak load duration min

Time constant min


1.18 1.38 1.45 1.14 1.32 1.36 1.11 1.25 1.28 1.17 1.49 1.54 1.14 1.40 1.45 1.12 1.32 1.36

0.5 0.7 0.9 0.5 0.7 0.9 0.5 0.7 0.9 0.5 0.7 0.9 0.5 0.7 0.9 0.5 0.7 0.9

120 60 30 120 60 30 120 60 30 120 60 30 120 60 30 120 60 30

15 30 60 15 30 60 15 30 60 45 90 180 45 90 180 45 90 180

40 30 20 40 30 20 40 30 20 40 30 20 40 30 20 40 30 20

Max hottest-spot temperature reached during load cycle °C 183 214 219 219 248 249 253 287 287 156 200 200 176 218 219 208 248 249

6.8 Other limitations

6.8.1 Magnetic leakage field in structural metallic parts The magnetic leakage field increases with increasing current. This field may cause excessive temperatures in structural metallic parts that may restrict the overloading. It should be noted that when the hot-spot temperature exceeds the highest temperature in Table 6 according to the insulation classes of the transformer, the characteristics of the insulation system may decrease to a level below the minimum value for the dielectric withstand of the transformer.

6.8.2 Accessories and other considerations Aside from the windings, other parts of the transformer, such as bushings, cable-end connections, tapchanging devices, the tap changer, temperature measurement devices, surge arresters, and leads may restrict the operation above the rated current.

6.8.3 Thermal relays A transformer thermal relay is a device that, when operated, indicates that predetermined time-temperature limits in the transformer windings have been reached. It is calibrated for use with specific transformer apparatus and automatically takes into account the hottest-spot temperature of the windings, the ambient temperature, and previous conditions of loading. Higher loads are permitted for short periods of operation than for long periods of operation. The relay can be adjusted to give indication at loads that can produce practically normal life expectancy or some predetermined moderate sacrifice of such expectancy. The device has one or more contacts that may be used for various functions, such as starting fans, giving a signal or an alarm, or disconnecting the transformers. 19




Annex A (informative) Bibliography Bibliographical references are resources that provide additional or helpful material but do not need to be understood or used to implement this standard. Reference to these resources is made for informational use only. [B1] den Outer, F. R., “The loading of solid-insulation distribution transformers with special reference to the cast resin type,” Proceedings of the International Conference on Electricity Distribution (CIRED 1977), London, Part I, pp. 75–79, Discussion Part II, pp. 31 –32, 37, 41–42, May 1977. [B2] Featheringill, W. E., “Power transformer loading,” IEEE Transactions on Industry Applications, vol. IA-19, no. 1, pp. 21–27, Jan./Feb. 1983. [B3] IEC 60076-12, Power Transformers—Part 12: Loading Guide for Dry-Type Power Transformers. 5 [B4] IEEE Std C57.12.59™, IEEE Guide for Dry-Type Transformer Through-Fault Current Duration. [B5] Montsinger, V. M., and Cooney, W. H., “Temperature rise of stationary electrical apparatus as influenced by radiation, convection, and altitude,” Annual Convention of the AIEE, Edgewater Beach, Chicago, IL, June 1924. [B6] National Oceanic and Atmospheric Administration National Climatic Data Center Climate Information.6 [B7] Pierce, L. W., “An investigation of the temperature distribution in cast-resin transformer windings,” IEEE Transactions on Power Delivery, vol. 7, no. 1, pp. 920–926, April 1992. [B8] Pierce, L. W., “Hottest spot temperatures in ventilated dry type transformers,” IEEE Transactions on Power Delivery, vol.9, no.1, pp. 257-264, January 1994. [B9] Pierce, L. W., “Predicting hottest spot temperatures in ventilated dry type transformer windings,” IEEE Transactions on Power Delivery, vol.9, no.2, pp. 1160-1172, April 1994. [B10] Pierce, L. W., “Thermal considerations in specifying dry-type transformers,” IEEE Transactions on Industry Applications, vol.30, no.4, pp. 1090-1098, July/August 1994. [B11] Pierce, L. W., “Transformer design and application considerations for nonsinusoidal load currents,” XXXVII Conference Record of the IEEE Cement Industry Technical Conference, pp. 35-47, June 1995. [B12] Ristow, R. J., and McCann, F. J., “Problems of impact loading on unit transformers supplying chipper motor drives,” Proceedings of the Sixteenth Annual IEEE Pulp and Paper Conference, June 1970. [B13] Whitman, L. C., “Loading of ventilated dry type transformers,” AIEE Transactions, vol. 76, Part III, pp. 1077–1084, December 1957.

5

IEC publications are available from the Sales Department of the International Electrotechnical Commission, 3 rue de Varembé, PO Box 131, CH-1211, Geneva 20, Switzerland (http://www.iec.ch/). IEC publications are also available in the United States from the Sales Department, American National Standards Institute, 25 West 43rd Street, 4th Floor, New York, NY 10036, USA (http://www.ansi.org). 6 Available at: http://www.ncdc.noaa.gov/climate-information

20




Annex B (informative) Computer programs

B.1 Short time loading based on nameplate rating

B.1.1 Code The following computer program coded in BASIC language is an example of how to calculate the data for short term loading. 10 REM THIS PROGRAM CALCULATES THE 20 REM SHORT TIME LOAD CAPABILITY OF 30 REM DRY-TYPE TRANSFORMERS 40 REM L1 = PRIOR PER UNIT LOAD 50 REM T1 = AMBIENT TEMPERATURE 60 REM T2 = RATED HOT SPOT RISE 70 REM T6 = MAXIMUM LIMITING HS TEMP 80 REM T9 = WINDING TIME CONSTANT, MIN. 90 REM HV & LV HAVE DIFFERENT TIME CONSTANTS 100 REM CHECK BOTH AND USE SHORTEST VALUE 110 READ L1,T1,T2,T6,T9 120 REM T3 = INITIAL HOTTEST-SPOT RISE 130 REM T4 = MAXIMUM LIMITING HS RISE 140 REM T5 = ULTIMATE HOTTEST-SPOT RISE 150 REM M = EXPONENT FOR HEATING 160 REM L2 = SHORT-TIME LOAD CAPABILITY 170 REM DEPENDS ON SELECTION 180 REM OF MAXIMUM LIMITING HS 190 REM TEMPERATURE, T6

21




200 OPEN "\CLCAP.TXT" FOR OUTPUT AS #1 210 PRINT #1,"PRIOR LOAD = ",L1 220 PRINT #1,"AMBIENT TEMPERATURE = ",T1 230 PRINT #1, "RATED HOTTEST-SPOT RISE = ",T2 240 PRINT #1,"MAX. LIMITING HS TEMP = ",T6 250 PRINT #1,"TIME CONSTANT, MINUTES = ",T9 260 T4 = T6 - T1 270 M = 0.8 280 T3 = T2*(L1^(2*M)) 300 PRINT #1,"SHORT-TIME LOAD CAPABILITY, SELF-COOLED" 310 PRINT #1," ","TIME, MIN.","LOAD, PU" 320 FOR T8 = 15 TO 240 STEP 15 330 X = 1 - EXP(-T8/T9) 340 T5 = ((T4 - T3)/X) + T3 350 X2 = 1/(2*M) 360 L2 = (T5/T2)^X2 370 IF L2>2 THEN L2 = 2 380 PRINT #1," ",T8,L2 390 NEXT T8 400 DATA 0.70,30,90,130,180 410 END

22




B.1.2 Example program output The following is sample program output from the code in B.1.1 PRIOR LOAD = 0.7 AMBIENT TEMPERATURE = 30 RATED HOTTEST-SPOT RISE = 90 MAX. LIMITING HS TEMP = 130 TIME CONSTANT, MINUTES = 180 SHORT-TIME LOAD CAPABILITY, SELF-COOLED TIME, MIN. LOAD, PU 15 2 30 2 45 2 60 1.769101 75 1.621648 90 1.519323 105 1.444161 120 1.386684 135 1.341396 150 1.304876 165 1.274882 180 1.249877 195 1.228774 210 1.21078 225 1.195303 240 1.18189

B.2 Loading above rating to give normal life expectancy during a one-day period The following computer program coded in BASIC language is an example of how to determine the aging of a dry-type transformer over a one-day period. The aging is based on some initial load less than 100% until temperature equilibrium is reached. The load is then increased to some value greater than 100% for some chosen period, after which the load is reduced to the original load value. Time intervals of 1 min are used to improve the calculation accuracy, and the summation of the age for 1440 1-min periods gives the daily total age in per unit of one day. The program may be used to determine for a given period what value the transformer may be overloaded and then allowed to return to the initial load without exceeding the equivalent aging of one day. This equivalent aging is the amount a transformer would undergo in a one-day period at 100% continuous load in a 30° ambient. 100 PRINT "TRANSFORMER EQUIVALENT AGING" 110 PRINT "THIS PROGRAM IS DESIGNED TO DETERMINE THE AGING OF A DRY-TYPE" 111 PRINT "TRANSFORMER OVER A ONE-DAY PERIOD OF TIME. THE TRANSFORMER" 112 PRINT "IS LOADED TO SOME INITIAL VALUE LESS THAN 100 PERCENT UNTIL" 113 PRINT "TEMPERATURE EQUILIBRIUM IS REACHED. THEN THE TRANSFORMER" 114 PRINT "IS LOADED GREATER THAN 100 PERCENT FOR SOME CHOSEN PERIOD" 115 PRINT "OF TIME. THE LOAD IS THEN REDUCED TO THE ORIGINAL VALUE."

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116 PRINT "" 117 PRINT "THIS PROGRAM WILL DETERMINE, FOR A GIVEN OVERLOAD" 118 PRINT "PERIOD, WHAT VALUE THE TRANSFORMER MAY BE OVERLOADED AND" 119 PRINT "THEN ALLOWED TO RETURN TO THE INITIAL LOAD WITHOUT EXCEEDING" 120 PRINT "THE EQUIVALENT AGING. THIS AGING IS EQUIVALENT TO THAT WHICH" 121 PRINT "A TRANSFORMER WOULD UNDERGO IN A ONE-DAY PERIOD AT 100 PERCENT" 122 PRINT "CONTINUOUS LOAD IN A 30 DEGREE AMBIENT." 130 PRINT "PARAMETERS ARE AS FOLLOWS:" 131 PRINT "A AND B VALUES ARE THE ARRHENIUS CONSTANTS IN BASE e" 132 PRINT "FOR A GIVEN INSULATION SYSTEM." 133 PRINT "C = RATED HOTTEST-SPOT TEMPERATURE RISE" 134 PRINT "DELT = 1 (MINUTE)" 135 PRINT "T = TIME (MINUTES)" 136 PRINT "TAU = TIME CONSTANT (MINUTES)" 137 PRINT "AMB = AMBIENT TEMPERATURE (CELSIUS)" 138 PRINT "LI = PER UNIT INITIAL LOAD LESS THAN 1.0" 139 PRINT "LU = PER UNIT OVERLOAD GREATER THAN 1.0" 140 PRINT "X = PERIOD OF TIME IN MINUTES THAT OVERLOAD OCCURS" 141 PRINT "RA = AGING FACTOR FOR DELT PERIOD OF TIME" 142 PRINT "SUMRA = PER UNIT AGE SUMMATION FOR 1440 MINUTES (ONE DAY)" 143 PRINT "WHEN SUMRA = 1.00, THEN THE CALCULATED AGING EQUALS" 144 PRINT " ONE DAY AT 100 PERCENT LOAD." 145 PRINT "TEMPI = INITIAL TEMP RISE DUE TO CONSTANT LOAD < 1.0" 146 PRINT "TEMPU = ULTIMATE TEMP RISE TRANSFORMER WOULD REACH IF OVERLOAD WERE" 147 PRINT "CONTINUOUSLY APPLIED" 148 PRINT "TEMPR = MAXIMUM TEMPERATURE RISE OF TRANSFORMER (CELSIUS)" 149 PRINT "NOTE: VALUE OF TEMPR IS PRINTED AT THE END OF OVERLOAD"

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150 PRINT "ABST = ABSOLUTE TEMPERATURE (CELSIUS)" 151 PRINT "TEMPF = FINAL TEMPERATURE AFTER 1440 MINUTES (CELSIUS)" 200 INPUT ; "A,B,C,TAU,AMB"; A, B, C, TAU, AMB 210 INPUT ; "LI = "; LI 220 INPUT ; "X = "; X 230 INPUT ; "LU = "; LU 240 T = 0 245 DELT = 1 250 SUMRA = 0 260 TEMPI = LI ^ 1.6 * C 270 PRINT "TEMPI = "; TEMPI 280 TEMPU = LU ^ 1.6 * C 290 PRINT "TEMPU = "; TEMPU 292 TAU1 = TAU * ((TEMPU - TEMPI) / ((TEMPU ^ 1.25) - (TEMPI ^ 1.25))) * C ^ .25 300 T = X 302 RD = EXP(-1 * T / TAU1) 304 RE = 1 - RD 310 TEMPR = (TEMPU - TEMPI) * RE + TEMPI 312 TAU2 = TAU * ((TEMPI - TEMPR) / ((TEMPI ^ 1.25) - (TEMPR ^ 1.25))) * C ^ .25 313 T = 0 314 FOR T = 0 TO X 315 RD = EXP(-1 * T / TAU1) 316 RE = 1 - RD 317 TEMPR = (TEMPU - TEMPI) * RE + TEMPI 320 ABST = TEMPR + 273.15 + AMB 322 RB = -1 * (A + B / ABST) 324 RC = 2.7183 ^ RB 330 RA = 122 * DELT * RC 25




340 SUMRA = SUMRA + RA 345 NEXT T 360 FOR T = X TO 1440 362 RF = -1 * (T - X) / TAU2 364 RG = EXP(RF) 366 RH = 1 - RG 370 TEMPF = (TEMPI - TEMPR) * RH + TEMPR 380 ABST = TEMPF + 273.15 + AMB 382 RB = -1 * (A + B / ABST) 384 RC = 2.7183 ^ RB 390 RA = 122 * DELT * RC 400 SUMRA = SUMRA + RA 410 NEXT T 420 PRINT "TEMPR = "; TEMPR 430 PRINT "TEMPF = "; TEMPF 440 PRINT "SUMRA = "; SUMRA 442 PRINT "TAU1 = "; TAU1 444 PRINT "TAU2 = "; TAU2 450 GOTO 230

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Annex C (informative) Example calculations

C.1 Overloads at constant temperature

C.1.1 Scenario Each resin-encapsulated transformer in a double-ended substation is loaded to 60% of capacity. A malfunction causes the removal of one transformer from the system and one unit is forced to supply both loads. The outage is expected to last ten days. What is the expected hottest-spot temperature and what is the estimated loss of life for the ten-day period of overload?

C.1.2 Assumptions The calculations in C.1.3 are based on the following assumptions: 

Insulation thermal class

220



Site ambient temperature

25 °C (constant)



Maximum rated ambient temperature

40 °C



Per unit overload (2 × 60%)

1.20



Length of time for overload

10 days

C.1.3 Calculations

C.1.3.1 Using Equation (1): Rated hottest-spot temperature rise over ambient = 220 – 40 = 180 °C

C.1.3.2 Using Equation (2): Hottest-spot temperature rise = 180 × 1.20 1.6 = 241 °C

C.1.3.3 Using Equation (1) and the constant site ambient temperature of 25 °C: Actual hottest-spot temperature = 25 + 241 = 266 °C As a crosscheck, the overload is within the guidelines, since the hottest-spot temperature does not exceed the recommended maximum temperature of 290 °C as shown in Table 6.

27




C.1.3.4 Using Equation (17) to calculate estimated loss of life The estimated loss of life due to this event is calculated using Equation (17) and the factors of Table 4 for a halving factor of 10 °C for the 220 insulation system.

Ln(a ) = −22.082 a = exp(− 22.082 ) = 2.570E − 10 b = 16 515 t Life = 2.57E − 10 × exp(16 515 (266 + 273.15)) = 5 165 h

C.1.3.5 Using Equation (17) for the rated hottest-spot temperature of 210 °C By comparison, using Equation (17) for the rated hottest-spot temperature of 210 °C results in:

t Life = 2.570E − 10 × exp(16 515 (210 + 273.15)) = 179 869 h

or approximately 180 000 h.

C.1.3.6 Calculation results Therefore, operation at a hottest-spot temperature of 266 °C, rather than the rated hottest-spot temperature of 210 °C, results in an accelerated loss of life by the ratio of 179 869/5 165, or 34.8 times the normal rate of loss of life. In other words, this is the equivalent of 34.8 h lost for each hour. Operating at the rated hottest-spot temperature of 210 °C, results in only 1 h of life lost for each hour of operation. 10 × 24 × 34.8 = 8 352 total equivalent hours of life lost during the ten-day or 240- h overload event. This is approximately equal to 8 352 /180 000 = 4.6% loss of life for this event. Normal loss of life for this same period would be approximately equal to: 240/180 000 = 0.13%

C.2 Short time overload for a step change in load

C.2.1 Scenario A solid-cast transformer is loaded to 50% of its capacity when it sees a step change in load for 2 h at the end of a 24-h period at 130% of rated capacity. What is the hottest-spot temperature after the 2-h event? What is the estimated loss of life for the overload period?



150




20 °C (constant)




40 °C

28






Per unit overload

1.30



Length of time for overload

2h



Shortest time constant for two windings

67 min

C.2.3 Calculations

C.2.3.1 Using Equation (1): The rated hottest-spot temperature rise over ambient = 150 – 40 = 110 °C

C.2.3.2 Using Equation (2) for initial hottest-spot temperature rise: The initial hottest-spot temperature rise = 110 × 0.5 1.6 = 36.3 °C.

C.2.3.3 Using Equation (2) for the ultimate hottest spot temperature rise: The ultimate hottest-spot temperature rise if allowed to stabilize = 110 × 1.30 1.6 = 167 °C

C.2.3.4 Using Equation (8):

( )( ) The adjusted time constant at overload = 67 × ( ) ( ) 167

110 1

−

36.3 110

1 167 0.8 36.3 0.8 − 110 110

= 67 × 0.828 = 55.5 min .

C.2.3.5 Using Equation (5): The hottest-spot temperature rise after the event = (167 – 36.3) × (1 – exp (-120/55.5)) + 36.3 = 152 °C. Adding the site ambient temperature of 20 °C, results in a hottest-spot temperature of 172 °C. The hottestspot temperature does not exceed the recommended maximum temperature of 175 °C. This is a quick check using a fixed time constant. A spread sheet calculation provides a more accurate picture using a dynamic time constant that changes with the changing winding temperature. The estimated loss of life may also be calculated using Equation (18) and the factors of Table 4 for a halving factor of 6. Ln(a) = -36.321 a = 1.683E-16 b = 20006

C.2.4 Calculation results Table C.1 shows the spreadsheet results of the calculations. The aging rate and the hottest-spot temperature are plotted in Figure C.1. The total loss of life over the 2-h period is equal to the area under the aging rate curve, which can be calculated several ways. The simple summation shown at the bottom of Table C.1 is

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the simplest calculation, but the accuracy depends on the size of the increment selected. In this case, an increment of 0.1 h, or 6 min, results in a loss of life of 136 h for the 2-h period. An increment of 1 min results in a summation of 135 h for the same period. Other options for estimating the area under the curve also include graphical estimation. Figure C.1 shows a dotted line drawn to approximate this area. The area of the triangle then is: Loss of life = 0.5 × 290 per unit × (2.0 – 1.12) h = 128 h Another method is to determine the equation of the line and then mathematically integrate the equation. However, in this case the equation is:

y = −29.739 x 4 + 179.57 x 3 − 196.17 x 2 + 62.204 x − 3.1245

Mathematical analysis becomes very difficult, and numerical integration methods such as the trapezoidal rule, Durand’s rule, and Simpson’s rule all lend themselves very well to computer analysis.

Table C.1— Tabulated calculations for step load change Time (h) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

Time constant (min) 67.0 55.5 54.2 53.1 52.3 51.6 51.0 50.5 50.1 49.8 49.5 49.2 49.0 48.8 48.7 48.5 48.4 48.3 48.2 48.1 48.1

Hottest-spot temperature rise (°C) 36.3 51.8 66.3 79.7 91.9 103 113 122 129 136 142 148 153 157 160 164 166 169 171 173 175

Hottest-spot Aging temperature rate (K) per unit 329 0.00000454 345 0.0000694 359 0.000723 373 0.00533 385 0.0292 396 0.124 406 0.421 415 1.20 422 2.93 429 6.28 435 12.1 441 21.2 446 34.4 450 52.3 453 75.0 457 103 460 135 462 170 464 209 466 250 468 292 Total loss of life in hours

Loss of lifetime (h) 0.000000454 0.00000694 0.0000723 0.000533 0.0 0292 0.0124 0.0421 0.120 0.293 0.628 1.21 2.12 3.44 5.23 7.50 10.3 13.5 17.0 20.9 25.0 29.2 136

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Figure C.1—Plot of aging calculation data

C.3 Life analysis with variable loads

C.3.1 Scenario A transformer has a repeating 24-h load cycle that includes variations in both the ambient temperature and the load. What is the maximum hottest-spot temperature achieved, and what is the estimated loss of life for the 24-h period? Normal loss of life would be 24 h.



180




variable




40 °C



Percent load

variable



Length of time for load period

24 h



Shortest time constant for two windings

25 min

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C.3.3 Calculations Spreadsheet analysis is well suited to more complicated combinations of varying load and ambient temperature. In this example, the first three columns of Table C.2 illustrate the time in increments of 1-h, the varying percent load, and the changing ambient temperature. The key results are also plotted in Figure C.2 and Figure C.3. The area under the aging curve is calculated using Simpson’s rule, which takes the following form:

AS

=

1 3

h [( y 0 + y n ) + 4( y1 + y 3

)

(

+  + y n −1 + 2 y 2 + y 4 +  + y n − 2

)]

where AS h y n

is the area by approximation, or the loss of life in this case, in hours is the time increment, in hours is aging rate is an even number

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Table C.2— Loss of life calculations for variable loads Time h

Load %


Ultimate hottest-spot temperature rise, °C

Time constant minutes

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

50 50 50 55 55 60 65 70 70 80 100 110 110 110 110 95 80 80 75 70 70 65 60 50 50

20 20 20 20 20 20 20 25 25 25 30 30 30 35 35 40 40 40 35 30 25 25 20 20 20

46.2 46.2 46.2 53.8 53.8 61.8 70.3 79.1 79.1 98.0 140. 163 163 163 163 129 98.0 98.0 88.4 79.1 79.1 70.3 61.8 46.2 46.2

26.4 33.0 33.0 31.8 31.8 30.7 29.7 28.8 28.8 27.3 25.0 24.1 24.1 24.1 24.1 25.5 27.3 27.3 28.0 28.8 28.8 29.7 30.7 33.0 33.0

Hottest-spot temperature rise achieved °C 46.5 46.2 46.2 52.6 53.6 60.7 69.0 77.9 79.0 95.8 136 161 163 163 163 132 102 98.4 89.5 80.4 79.3 71.5 63.2 48.9 46.6

Hottest -spot temperature °C 66.5 66.2 66.2 72.6 73.6 80.7 89.0 103 104 121 166 191 193 198 198 172 142 138 124 110 104 96.5 83.2 68.9 66.6

Aging rate per unit

Simpson’s factor

Simpson’s expansion

0.0000696 0.0000674 0.0000670 0.000144 0.000161 0.000359 0.000888 0.00366 0.00408 0.0198 0.750 4.09 4.67 6.48 6.48 1.17 0.118 0.0895 0.0275 0.00759 0.00421 0.00193 0.000474 0.0000932 0.0000706

1 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 2 4 1

6.96E-05 0.000269 0.000134 0.000576 0.000323 0.00144 0.00178 0.0146 0.00816 0.0794 1.50 16.4 9.34 25.9 13.0 4.67 0.236 0.358 0.0551 0.0304 0.00842 0.00772 0.000948 0.000373 0.0000706 71.6 23.8

Total loss of life in hours

The maximum hottest-spot temperature achieved during the loading period is 198 °C, which is well below the 250 °C limit recommended in Table 6 for a resin-encapsulated transformer. The estimated loss of life is 23.85 h or nearly one day for the 24-h period.

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